While the markets had been hoping to see a March thaw, a heavy calendar of February data in the week ahead is likely to show the economy is still feeling a bit chilled.
The jobs report is the big number, released Friday and expected to show about 150,000 nonfarm payrolls and an unchanged unemployment rate of 6.6 percent.
If weak, it would be the third in a row to show a slower pace of job growth than last year's trend of closer to 200,000. If it misses. it could again be blamed on unusually severe winter weather.
"The whisper is for weaker," said Tony Crescenzi, strategist and portfolio manager at Pimco. "Markets are braced for a weaker one. ... Strength would not be dismissed but whereas markets would see through weakness, they would take strength at face value." One reason is that there were storms during the survey week for the jobs report.
March's weather might be roaring in like a lion, but the stock market is prancing in like a lamb.
With the S&P 500 at an all-time high and the Dow within striking distance of its high, this March is special in that it's now been five years since the market bottomed. The S&P 500 on March 9, 2009, plunged to the very memorable—and very painful—666 level.
The markets will stay focused on developments in Ukraine, as traders worry that Russia could become more strident, prompting action from Western governments. Reports Friday that Russian troops were in Crimea spooked the market, and wiped out its sharpest gains.
(Read more: Obama: US 'deeplyconcerned' by Crimea situation)
The S&P closed at 1,859.45 on Friday, up 76.86 points or 4.31 percent for the month, its largest gain since October 2013. The Dow ended at 16,321.71 up 3.97 percent in February and now within 266 points of its all-time high. The Nasdaq ended the month at 4,308.12, up 5 percent.
For the week, the S&P rose 1.26 percent, while the Dow gained 1.36 percent, and the Nasdaq increased 1 percent—the only of the three major indexes to increase for four consecutive weeks.
But even so, analysts see further gains, and CEOs are showing more signs of confidence.
Merger activity is at pre-crisis levels, and there's a flurry of IPO activity. At least four IPOs are expected in the coming week, including Coupon.com, an online coupon site.
(Read more: Jobless rate to dip below 6% in 2014: Fed's Bullard)
"We think it has a ways to run. I don't think we're going to have that same kind of pace," said Ed Keon of Quantitative Management Associates. "We're coming up on the five-year anniversary, and we have had 25 percent annualized returns. That pace is not sustainable." Keon said he expects the market to be up about 10 percent this year.
"The market has pretty well decided, and I agree, that some of the weak economic data we've seen in the last couple of months was largely driven by the terrible weather much of the country has had, and it's also likely to impact earnings for the first quarter," said Keon. "You're going to get a weak first-quarter GDP, but I think you'll see plus 3 percent growth for the year overall."
(Read more: US economy lost steam in fourth quarter)
Companies have already been warning about weather impact, and analysts are already shaving earnings estimates. Christian Wetherbee follows railroads at Citigroup, and he chopped 6 percent off first-quarter earnings estimates for the industry because of weaker volumes and higher costs from bad weather.
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Wetherbee said those estimates take into account the first two months of the year, and March is a wild card, possibly knocking earnings even lower if the weather stays bad.
Retailers have been reporting weather impact, and several report earnings this week, including Costco and Staples.
The jobs report is the big item for markets in the coming week because it is so key to Fed policy. Fed Chair Janet Yellen has said the weather may indeed be a factor in weak employment, and the softer economy in general, and traders are watching to see whether it really is just weather effect or some other factors causing economic slowing.
"Nonfarm payrolls is the big one, but so are auto sales and manufacturing PMI. Those are the three big reports next week and ideally we'd like to see all of them show better than expectations," said Marc Chandler, chief currency strategist for Brown Brothers Harriman.
Auto sales are reported Monday, as is ISM manufacturing and manufacturing PMI.
(Read more: Retail stuck in double helix: Soft sales, margins)
"As far as the data, up until this week, almost every piece of data came in below expectations, and the market didn't appreciate the magnitude of the slowdown, but now we've had durable goods orders, Chicago PMI, better than expected, and new home sales better than expected. These are secondary releases. That's why next week's data is going to be important," said Chandler.
Chandler said markets will also be watching the European Central Bank, which meets Thursday. There is speculation the ECB will cut its 0.25 percent repo rate, but Chandler said the ECB would get more bang if it cuts the lending rate. "They could change the ceiling, cut their lending rate—currently 75 basis points, cut it to 50 basis points," he said.
Investors will also be watching for investor Warren Buffett's letter to investors, to be released this Saturday.