Here's the reg in question. I bolded sub-parts B and D. Section B only states what must be done to move to Phase II (controllable and not hazardous). Sub-part D is more pertinent to this conversation. In particular, Paragraph 2 states: "Operate under VFR, day only, unless otherwise specifically authorized by the Administrator." When the DAR issues the airworthiness certificate, a set of operating limitations is also issued. They state what operations can and cannot be done in Phase I and II. Going strictly on memory, I believe Phase I normally states that IFR flight is not allowed. However, Phase II has wording similar to, "VFR only unless equipped in accordance with CFR 14 91.xxx." There is similar wording for night flight. That is the "unless otherwise specifically authorized by the Administrator" part.

So, my conclusion is that no IFR flight is allowed during Phase I, but assuming your aircraft is properly equipped, IFR flight IS allowed during Phase II.

I don't recall anything being mentioned in the operating specifications about flight in icing conditions, but I'd be interested to get an authoritative answer on it. Or at least some guidance on how to go about it without renting some heavy aircraft to spray me down in freezing temperatures.

Sec. 91.319 Aircraft having experimental certificates: Operating limitations.

(a) No person may operate an aircraft that has an experimental
certificate--
(1) For other than the purpose for which the certificate was issued;
or
(2) Carrying persons or property for compensation or hire.
(b) No person may operate an aircraft that has an experimental
certificate outside of an area assigned by the Administrator until it is
shown that--
(1) The aircraft is controllable throughout its normal range of
speeds and throughout all the maneuvers to be executed; and
(2) The aircraft has no hazardous operating characteristics or
design features.
 (c) Unless otherwise authorized by the Administrator in special
operating limitations, no person may operate an aircraft that has an
experimental certificate over a densely populated area or in a congested
airway. The Administrator may issue special operating limitations for
particular aircraft to permit takeoffs and landings to be conducted over
a densely populated area or in a congested airway, in accordance with
terms and conditions specified in the authorization in the interest of
safety in air commerce.
(d) Each person operating an aircraft that has an experimental
certificate shall--
(1) Advise each person carried of the experimental nature of the
aircraft;
(2) Operate under VFR, day only, unless otherwise specifically
authorized by the Administrator; and
(3) Notify the control tower of the experimental nature of the
aircraft when operating the aircraft into or out of airports with
operating control towers.
(e) No person may operate an aircraft that is issued an experimental
certificate under Sec. 21.191(i) of this chapter for compensation or
hire, except a person may operate an aircraft issued an experimental
certificate under Sec. 21.191(i)(1) for compensation or hire to--
(1) Tow a glider that is a light-sport aircraft or unpowered
ultralight vehicle in accordance with Sec. 91.309; or
(2) Conduct flight training in an aircraft which that person
provides prior to January 31, 2010.
(f) No person may lease an aircraft that is issued an experimental
certificate under Sec. 21.191(i) of this chapter, except in accordance
with paragraph (e)(1) of this section.
(g) No person may operate an aircraft issued an experimental
certificate under Sec. 21.191(i)(1) of this chapter to tow a glider
that is a light-sport aircraft or unpowered ultralight vehicle for
compensation or hire or to conduct flight training for compensation or
hire in an aircraft which that persons provides unless within the
preceding 100 hours of time in service the aircraft has--
(1) Been inspected by a certificated repairman (light-sport
aircraft) with a maintenance rating, an appropriately rated mechanic, or
an appropriately rated repair station in accordance with inspection
procedures developed by the aircraft manufacturer or a person acceptable
to the FAA; or
(2) Received an inspection for the issuance of an airworthiness
certificate in accordance with part 21 of this chapter.
(h) The FAA may issue deviation authority providing relief from the
provisions of paragraph (a) of this section for the purpose of
conducting flight training. The FAA will issue this deviation authority as a letter of
deviation authority.
(1) The FAA may cancel or amend a letter of deviation authority at
any time.
(2) An applicant must submit a request for deviation authority to
the FAA at least 60 days before the date of intended operations. A
request for deviation authority must contain a complete description of
the proposed operation and justification that establishes a level of
safety equivalent to that provided under the regulations for the
deviation requested.
(i) The Administrator may prescribe additional limitations that the
Administrator considers necessary, including limitations on the persons
that may be carried in the aircraft.